Question

For a randomly selected driver, are the events "driving while using a cell phone" and "having a traffic accident" independent events? Explain your answer. PLEASE HELP :(

Answer 1

Let's denote:

The event of driving while using a cell phone: A

The event of having a traffic accident: B

The event of driving while using a cell phone and having a traffic accident: A⋂B

P(A) = 11% = 0.11

P(B) = 5.26% = 0.526

P(A⋂B) = 28% = 0.28

If event A and event B are independent (it means the cause of a traffic accident is nothing related to driving while using a cell phone), then:

P(A) x P(B) = P(A⋂B)

Let's check:

P(A) x P(B) = 0.11 x 0.526 = 0.05786 and not equal to P(A⋂B) = 0.28

=> Event A and event B are not independent. In other words, they are related. (it means driving while using a cell phone is one of the reasons for having a traffic accident)